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This paper report on a low-loss, broadband, and tunable negative refractive index metamaterial (NRIM) consisting of yttrium iron garnet (YIG) slabs and printed circuit boards (PCBs). The YIG slabs under an applied magnetic field provide a negative permeability and the PCBs provide a negative permittivity. The substrates of the PCBs decuple the interactions between the YIG slabs and wire array deposed on such substrates. The effective electromagnetic parameters of the NRIM and the conditions of exhibiting the negative refractive index character are analyzed theoretically. Then the negative transmission and negative refraction characters are investigated numerically and experimentally. The results indicate that the NRIM exhibits negative pass band within the X-band with a bandwidth of about 1 GHz and a peak transmission power of about - 2.5 dB. While changing the applied magnetic field from 2300 Oe to 2700 Oe, the measured pass band of NRIM shift from 8.42 GHz to 9.50 GHz with a 2.7 MHz/Oe step. The results open a sample way to fabricate the NRIM, further, the metamaterial cloak and absorber.

Since the negative refractive index metamaterial (NRIM) predicted by Veselago [

In order to fabricate a broadband and tunable NRIM, the SRR structure resulting in the narrow band and untunability must be replaced by some other structures or materials. Some researchers proposed ferrimagnet based NRIM, that is, substitute ferrimagnet such as yttrium iron garnet (YIG) for the SRR structure to obtain the negative permeability [18–22]. Dewar gave the theoretical expressions of the effective parameters and analyzed the interaction of the ferrites and wires [

The aim of this work is to provide a low-loss, broadband, and tunable NRIM consisting of YIG slabs and printed circuit boards (PCBs). The YIG slabs under applied magnetic field give rise to a negative permeability and the PCBs provide a negative permittivity. This NRIM is designed because there are some advantages. For instance, it can be easily fabricated with YIG slabs and PCBs. The thickness of the wire depositing on PCBs has a very small value so that the frequency band in which the refraction index is negative can be achieved to far infrared and optical frequencies. And the interaction between YIG slabs and wires can be easily reduced by using the substrate layers.

In this paper we present the model of the NRIM and give the fabricated parameter values based on the theoretical analysis. Then we give the approximate theoretical results of the effective permeability and permittivity of the NRIM. The EM transmission properties are numerically investigated by using ANSOFT’s High Frequency Structure Simulator (HFSS) tools. In the end we experimentally investigate the negative transmission, tunability, and negative refraction properties by testing the NRIM sample in X-band rectangular waveguide.

To design a low-loss, broadband, and tunable NRIM, the ferrimagnet is used to replace the SRR structures to provide the negative permeability. The PCBs are used to obtain the negative permittivity. The ferrimagnet has some particular properties. For instance, the loss in ferrimagnet is much smaller than typical conductor SRR [

Consequently, based on the above analysis, the schematic of the NRIM is designed and presented in ^{3}, a saturation magnetization of 1830 Gs (1 Gs = 10^{3}/(4p) A/m), and a line width of about 22 Oe (1 Oe =10^{3}/(4p) A/m). The substrates of PCBs, which are made from RT/duriod 5880 glass microfiber reinforced PTFE composites, are used to reduce the interaction between YIG slabs and wire array. Each PCB has a dimension of 22.86 × 10.16 ×0.254 mm^{3}. The wires depositing on the substrates have a dimension of 0.2 × 10.16 × 0.018 mm^{3} and periodic distance of 1.508 mm along the x axis. There are one layer PCB and one layer substrate in per two YIG slabs, as shown in

In this section we briefly show the theoretical analysis of the NRIM presented in Section 2. We mainly focus on the effective permeability and permittivity which describe the macroscopical characters of the composite NRIM. Dewar have analyzed the theoretical results of the effective permeability of the ferrimagnet under applied magnetic field and the effective permittivity of the wire array surrounded with a dielectric material in the ferrimagnetic host [

Here Ms is saturation magnetization of YIG. γ is gyromagnetic ratio. Λ is a phenomenological damping parameter describing loss intrinsic to the magnetic material [_{0} is the applied magnetic field. ε_{f} is the permittivity of ferrite. σ_{eff} is the effective conductivity of wire arrays. ε_{0} is the permeability of air. ω is the angular frequency. r_{1} is the radius of the wire. r_{2} is the radius of the insulated layer. And a is the periodic lattice constant. Using the equations presented above and parameter values presented in Section 2, the effective permeability and permittivity are calculated and shown in

It can be found from _{eff} and permittivity ε_{eff} exhibit typical resonant character. In the broad range from 9.18 GHz to 11.5 GHz both the real part of μ_{eff} and ε_{eff} are negative, so the EM wave can be propagated in such medium. Moreover the bandwidth can be expanded further by choosing different YIG slabs and designing dimensions of the wire array. The image parts of the two parameters, which show the loss in the medium, are much smaller and approximately equal to 0. Moreover, as shown in _{eff} increase from 8.66 to 9.85 GHz as H_{0} rises from 2300 to 2700 Oe. So the NRIM presented in this paper can be tuned by changing the applied magnetic field.

In this section, we first investigate numerically the EM properties of the designed NRIM shown in

To numerically simulate the transmission properties of the NRIM under the incidence of TEM waves, we use a planar waveguide system with a cross section of 22.86 × 10.16 mm^{2}. The NRIM is put at the middle of planer waveguide with the perfect E boundaries at up and down sides and the Master and Slave boundaries at the left and right sides. Here we simulate two cases.

Case (1): An EM wave propagated along the z axis with an electric field along the y axis and magnetic field along the -x axis, and a dc applied magnetic field along the y axis. The parameter values used to simulation are the same as Section 3. The simulated magnitudes of S_{11} and S_{21} of the NRIM under the applied magnetic field of 2300 Oe are shown in

Case (2): The EM wave propagated along the x axis with the electric field along the y axis and the magnetic field along the z axis, and the dc applied magnetic field along the y axis. The parameters values are the same as Section 3 too. The simulated magnitudes of the S_{11} and S_{21} of the NRIM under the applied magnetic field of 2300 Oe are shown in

At the same time, the magnitudes of the S_{21} of the NRIM in case (2) under a series of values of the applied magnetic fields are simulated and are shown in

In case (1), as shown in

is about -8 dB, and the bandwidth is about 1 GHz. The green lines in

The simulated results show that the loss of the composite presented here is much smaller than other NRIMs [2,4–9]. The loss of NRIM is generally come from ohmic loss of wires and dielectric loss of substrates. Replacement of the cut-ring structures [

So the bandwidth can be expanded and the center frequency can be improved by choosing the YIG slabs of bigger saturation magnetization. From Equations (1)–(3) we can also know that the tunability of the NRIM is dependent on the tunability of negative permeability in the YIG slabs. The wire array has a negative permittivity within a wide frequency region below the plasma frequency [

In order to confirm experimentally the conclusions presented in Section 3 and the numerical results presented above, we fabricated the NRIM sample to measure experimentally the transmission character and also fabricated the prism-shaped prototype to determine the refractive index via the Snell’s law.

In practice, the NRIM sample consisting of YIG slabs and PCBs is shown in _{21} of the NRIM sample and the YIG slabs under the applied magnetic field of 2500 Oe and PCBs were measured using the network analyzer at X-band, were shown in

It can be seen from _{21} shifted from 8.42 GHz to 9.50 GHz with the sensitively tuning rate of 2.7 MHz/Oe.

For the refraction experiment, we fabricated a prismshaped NRIM sample inserted in

As can be seen in _{Paraffin} = 1.5 ± 0.1, whereas for the NRIM, the measured exit angle of θ = -32° implies that n_{NRIM} = -1.6 ± 0.1.

In conclusion, a low-loss, broadband, and tunable negative refractive index metamaterial consisting of YIG slabs and PCBs is designed and fabricated. Both the simulated and experimental properties of NRIM are investigated. The simulated scattering parameters of the NRIM indicate that there is a pass band in the X-band and the bandwidth is about 1 GHz and the pass band can be shifted by changing the magnetic field. Besides, the experimentally measured scattering parameters show that there is a pass band within the forbidden band of both the YIG slabs and PCBs. The magnitude of S_{21} shifted from 8.42 GHz to 9.50 GHz with the sensitively tuning rate of 2.7 MHz/Oe when changing the applied magnetic field from 2300 Oe to 2700 Oe. Both the simulated results and the experimentally measured results verify the correctness of the designed NRIM. The results open a sample way to fabricate NRIM, further, the metamaterial cloak and absorber.

This work was supported by the National Science Foundation of China under Grant Nos. 60571024, 60771046, and 60588502.